5 days of golf for 24 players

[Greg Grodzicki(Guest)]

Richard,

Can you help me?

Need a schedule for a five day golf event for 24 golfers.  The golfers are divided into two teams (Ryder Cup style). I need a schedule so the six foursomes never play with the same players twice (even fellow teammates), yet are divided into two teammates of one team versus two teammates of the other team.
Hope you can help.

Wednesday, July 27 2005, 11:45 am
Livonia , Michigan

[Ian Wakeling]

Greg,

The following is a solution to your question.

In the schedule below, I have labelled the 2 teams of 12 players A1-A12 and B1-B12.

Over the 5 rounds, the foursomes are arranged so that all have exactly 2 players from each team, that each team member plays with 5 different members of their own team, and plays against 10 different players from the 12 on the opposing team.

Round	Teams
1	(A6, A10,B2, B7 ) (A9, A11,B9, B11) (A5, A8, B4, B10) (A1, A4, B5, B6 ) (A3, A7, B8, B12) (A2, A12,B1, B3 )
2	(A2, A3, B6, B9 ) (A7, A8, B2, B11) (A5, A9, B3, B8 ) (A10,A12,B5, B12) (A1, A6, B1, B4 ) (A4, A11,B7, B10)
3	(A1, A9, B2, B12) (A8, A12,B7, B9 ) (A3, A6, B3, B10) (A2, A5, B5, B11) (A4, A10,B1, B8 ) (A7, A11,B4, B6 )
4	(A5, A12,B2, B6 ) (A4, A6, B9, B12) (A1, A2, B7, B8 ) (A3, A10,B4, B11) (A7, A9, B1, B10) (A8, A11,B3, B5 )
5	(A7, A10,B3, B9 ) (A3, A9, B5, B7 ) (A1, A12,B10,B11) (A2, A4, B2, B4 ) (A6, A8, B6, B8 ) (A5, A11,B1, B12)

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I am fairly certain that it is impossible to find a similar schedule for 6 rounds.

Regards,
Ian.

Friday, October 7 2005, 11:35 am

[Jbrown56]

Ian,

What would the solution be for 2 teams of 14 players each?

Thanks,

Jeff

[Ian Wakeling]

Jeff,

This is a nicer problem than the 2 teams of 12 above as it is possible to have a schedule for the full 7 rounds, with every players playing exactly 7 different members of their own team, and all 14 players on the opposing team.

Round	Teams
1	(A1, A8, B1, B8 ) (A2, A10,B4, B12) (A3, A12,B7, B9 ) (A4, A14,B3, B13) (A5, A9, B6, B10) (A6, A11,B2, B14) (A7, A13,B5, B11)
2	(A2, A9, B2, B9 ) (A3, A11,B5, B13) (A4, A13,B1, B10) (A5, A8, B4, B14) (A6, A10,B7, B11) (A7, A12,B3, B8 ) (A1, A14,B6, B12)
3	(A3, A10,B3, B10) (A4, A12,B6, B14) (A5, A14,B2, B11) (A6, A9, B5, B8 ) (A7, A11,B1, B12) (A1, A13,B4, B9 ) (A2, A8, B7, B13)
4	(A4, A11,B4, B11) (A5, A13,B7, B8 ) (A6, A8, B3, B12) (A7, A10,B6, B9 ) (A1, A12,B2, B13) (A2, A14,B5, B10) (A3, A9, B1, B14)
5	(A5, A12,B5, B12) (A6, A14,B1, B9 ) (A7, A9, B4, B13) (A1, A11,B7, B10) (A2, A13,B3, B14) (A3, A8, B6, B11) (A4, A10,B2, B8 )
6	(A6, A13,B6, B13) (A7, A8, B2, B10) (A1, A10,B5, B14) (A2, A12,B1, B11) (A3, A14,B4, B8 ) (A4, A9, B7, B12) (A5, A11,B3, B9 )
7	(A7, A14,B7, B14) (A1, A9, B3, B11) (A2, A11,B6, B8 ) (A3, A13,B2, B12) (A4, A8, B5, B9 ) (A5, A10,B1, B13) (A6, A12,B4, B10)

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Note that above you can partition the two teams into subgroups of 7. Namely A1-A7, A8-A14, B1-B7 and B8-B14. Players within a subgroup never play together.  This could be used to balance the mixture of abilities in the foursomes by always putting forward a lower and higher handicap player from each team.

Hope that helps,

Ian.

[Jbrown56]

Ian,

This year our tournament consists of 2 teams of 16 players each? Could you please add the solutions for that?

Thanks,

Jeff

[Ian Wakeling]

Hi Jeff,

I think the schedule below should work for your next tournament.  It has the same properties as the 2 teams of 14 schedule above and everyone would play with all members of the opposing team if you have time to play 8 rounds.

Ian.

Round	Teams
1	(A1 A9  B1 B9 ) (A2 A11 B4 B13) (A3 A13 B7 B12) (A4 A15 B6 B16) (A5 A12 B8 B15) (A6 A10 B5 B11) (A7 A16 B2 B14) (A8 A14 B3 B10)
2	(A2 A10 B2 B10) (A1 A12 B3 B14) (A4 A14 B8 B11) (A3 A16 B5 B15) (A6 A11 B7 B16) (A5 A9  B6 B12) (A8 A15 B1 B13) (A7 A13 B4 B9 )
3	(A3 A11 B3 B11) (A4 A9  B2 B15) (A1 A15 B5 B10) (A2 A13 B8 B14) (A7 A10 B6 B13) (A8 A12 B7 B9 ) (A5 A14 B4 B16) (A6 A16 B1 B12)
4	(A4 A12 B4 B12) (A3 A10 B1 B16) (A2 A16 B6 B9 ) (A1 A14 B7 B13) (A8 A9  B5 B14) (A7 A11 B8 B10) (A6 A13 B3 B15) (A5 A15 B2 B11)
5	(A5 A13 B5 B13) (A6 A15 B8 B9 ) (A7 A9  B3 B16) (A8 A11 B2 B12) (A1 A16 B4 B11) (A2 A14 B1 B15) (A3 A12 B6 B10) (A4 A10 B7 B14)
6	(A6 A14 B6 B14) (A5 A16 B7 B10) (A8 A10 B4 B15) (A7 A12 B1 B11) (A2 A15 B3 B12) (A1 A13 B2 B16) (A4 A11 B5 B9 ) (A3 A9  B8 B13)
7	(A7 A15 B7 B15) (A8 A13 B6 B11) (A5 A11 B1 B14) (A6 A9  B4 B10) (A3 A14 B2 B9 ) (A4 A16 B3 B13) (A1 A10 B8 B12) (A2 A12 B5 B16)
8	(A8 A16 B8 B16) (A7 A14 B5 B12) (A6 A12 B2 B13) (A5 A10 B3 B9 ) (A4 A13 B1 B10) (A3 A15 B4 B14) (A2 A9  B7 B11) (A1 A11 B6 B15)

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